Damping devices of this type are state of the art. Such hydraulic dampers, which are also known as sound dampers or silencers, serve to reduce vibrations produced by pressure pulsations. Pressure pulsations are periodically applied to a corresponding hydraulic system, in particular as a result of the operation of hydraulic pumps. As is disclosed in document DE 102 17 080 C1, the known damping devices of this type have a damping housing in the form of a circular cylinder. The circular cylinder is rounded in a spherical manner, for example, at both axial end regions, with the fluid inlet and the fluid outlet being located coaxial to the cylinder axis on a respective end region. For the reduction of noise created by vibrations produced by pressure pulsations, which reduction is realized by a Helmholtz resonator, the damping housing is radially expanded at least in regions relative to the damping tube determining the flow direction. A space containing a Helmholtz volume is then formed, which volume the damping tube is connected to via the at least one branch opening.